Relative lipschitz-like property of parametric systems via projectional coderivatives
Siam Journal on Optimization(2023)
摘要
This paper concerns upper estimates of the projectional coderivative of implicit mappings and corresponding applications on analyzing the relative Lipschitz-like property. Under different constraint qualifications, we provide upper estimates of the projectional coderivative for solution mappings of parametric systems. For the solution mapping of affine variational inequalities, a generalized critical face condition is obtained for sufficiency of its Lipschitz-like property relative to a polyhedral set within its domain under a constraint qualification. The necessity is also obtainable under some regularity or when the polyhedral set is further the domain of the solution mapping. We further discuss possible conditions for the necessity and consider the solution mapping of a linear complementarity problem with a Q0 matrix as an example.
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关键词
parametric systems,relative Lipschitz-like property,generalized Mordukhovich criterion,affine variational inequality,linear complementarity problem
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